NEITHER. The back panel is not supposed to come off on this washer and working from the bottom requires you to tilt the washer backwards which can cause the gearcase (transmission) oil to leak through the top breather hole. You need to remove the exterior washer case in order to gain full access to the motor coupling. The procedure is much simpler, then it sounds. the following link explains:

Your washer is manufactured by Whirlpool, so these instrucitons do apply. The part number for a replacement coupling is inlcuded in the link I provided. Replacements can be purchased at any of the following websites:

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The motor coupler is broken and the black round rubber piece you found under the washer is the rubber grommet that connects the coupler parts. The six plastic teeth are the coupler prongs, 3 for each coupler part. Replace the motor coupler.

Disconnect power and release the console from the top of the cabinet depending on the model of your machine then pull forward and up on the
console and lay it back on the hinges.

Disconnect the lid switch harness connector by pressing on the tab
located in the middle and pulling it up.

The cabinet is attached
to the rear of the washer by
two brass-colored
retaining clips. Insert a flat blade screwdriver into the turned-up edge
of the clip, located on both sides, and then pry back to release the
clip from the slot in the cabinet.

Open and hold the lid while grabbing
the cabinet front opening then tilt the top of the cabinet toward you by
pulling the cabinet away from the base. This releases the front and
back slots of the cabinet from the tabs in the front and back of the
base. Using the side of your leg and/or body as a support for the front
of the cabinet, carefully lift up and set the cabinet aside.

With the cabinet removed, pry the clips securing the pump to the motor off and remove the pump.

Disconnect the motor harness then remove the
screw securing the bottom clip holding the motor and remove the clip.
Hold the motor from the bottom while loosening the screw securing the
top clip holding the motor. Remove the clip then pull the motor out of
the washer.

Remove the broken coupler parts from the transmission
and the motor
shaft then tap the new coupler parts in place or until the splines are
even with the edge of the coupler.

Remove the motor mounting plate to remove the coupler part in the transmission side more easily.

Once the coupler parts are properly installed, put the rubber grommet into the
coupler in the motor then line up the remaining slots on the grommet
with the coupler prongs in the transmission and put them together.

Secure the motor with the clips and the clips with the screws then
reconnect the motor wiring harness to the motor terminals and reinstall the pump in reverse order of the removal steps.

Bring the cabinet to the front of the washer then slide the front bottom rail of the cabinet under the rail at the
base
of the machine then lay down the cabinet into position. Make sure the
slots in the cabinet sit into the tabs at the base of machine.

Reconnect
the lid switch harness then push the retaining clips back down into position
to secure the cabinet to the rear of the machine. Reinstall and secure
the console to complete the repair.

This is a clear evidence of a broken motor coupler. It is the one that connects the drive motor shaft to the transmission assembly and transfer the
mechanical energy of the motor. The mechanical energy is not transferred to the transmission
and therefore result in the agitator not to agitate and the drum not to
spin. The drain pump works because it is directly coupled to the rear
spline of the motor. Replace the motor coupler to address the problem.

Release the console from the top of the cabinet depending on the model of your machine then pull forward and up on the
console and lay it back on the hinges.

Disconnect the lid switch harness connector by pressing on the tab
located in the middle and pulling it up.

The cabinet is attached
to the rear of the washer by
two brass-colored
retaining clips. Insert a flat blade screwdriver into the turned-up edge
of the clip, located on both sides, and then pry back to release the
clip from the slot in the cabinet.

Open and hold the lid while grabbing
the cabinet front opening then tilt the top of the cabinet toward you by
pulling the cabinet away from the base. This releases the front and
back slots of the cabinet from the tabs in the front and back of the
base. Using the side of your leg and/or body as a support for the front
of the cabinet, carefully lift up and set the cabinet aside.

With the cabinet removed, pry the clips securing the pump to the motor off and remove the pump.

Disconnect the motor harness then remove the
screw securing the bottom clip holding the motor and remove the clip.
Hold the motor from the bottom while loosening the screw securing the
top clip holding the motor. Remove the clip then pull the motor out of
the washer.

Remove the broken coupler parts from the transmission
and the motor
shaft then tap the new coupler parts in place or until the splines are
even with the edge of the coupler.

Remove the motor mounting plate to remove the coupler part in the transmission side more easily.

Once the coupler parts are properly installed, put the rubber grommet into the
coupler in the motor then line up the remaining slots on the grommet
with the coupler prongs in the transmission and put them together.

Secure the motor with the clips and the clips with the screws then
reconnect the motor wiring harness to the motor terminals and reinstall the pump in reverse order of the removal steps.

Bring the cabinet to the front of the washer then slide the front bottom rail of the cabinet under the rail at the
base
of the machine then lay down the cabinet into position. Make sure the
slots in the cabinet sit into the tabs at the base of machine.

Reconnect
the lid switch harness then push the retaining clips back down into position
to secure the cabinet to the rear of the machine. Reinstall and secure
the console to complete the repair.

This is a clear evidence of a broken motor coupler. The
mechanical output of the motor is not transferred to the transmission
and therefore result in the agitator not to agitate and the drum not to
spin. It drains because the drain pump is directly coupled to the rear
spline of the motor. Replace the motor coupler to address the problem.

Release the console from the top of the cabinet depending on the model of your machine then pull forward and up on the
console and lay it back on the hinges.

Disconnect the lid switch harness connector by pressing on the tab,
located in the middle, and pulling it up.

The cabinet is attached
to the rear of the washer by
two brass-colored
retaining clips. Insert a flat blade screwdriver into the turned-up edge
of the clip, located on both sides, and then pry back to release the
clip from the slot in the cabinet.

Open and hold the lid while grabbing
the cabinet front opening then tilt the top of the cabinet toward you by
pulling the cabinet away from the base. This releases the front and
back slots of the cabinet from the tabs in the front and back of the
base. Using the side of your leg and/or body as a support for the front
of the cabinet, carefully lift up and set the cabinet aside.

With the cabinet removed, pry the clips securing the pump to the motor off and remove the pump.

Disconnect the motor harness then remove the
screw securing the bottom clip holding the motor and remove the clip.
Hold the motor from the bottom while loosening the screw securing the
top clip holding the motor. Remove the clip then pull the motor out of
the washer.

Remove the broken coupler parts from the transmission
and the motor
shaft then tap the new coupler parts in place or until the splines are
even with the edge of the coupler.

Remove the motor mounting plate to remove the coupler part in the transmission side more easily.

Once the coupler parts are properly installed, put the rubber grommet into the
coupler in the motor then line up the remaining slots on the grommet
with the coupler prongs in the transmission and put them together.

Secure the motor with the clips and the clips with the screws then
reconnect the motor wiring harness to the motor terminals and reinstall the pump.

Bring the cabinet to the front of the washer then slide the front bottom rail of the cabinet under the rail at the
base
of the machine then lay down the cabinet into position. Make sure the
slots in the cabinet sit into the tabs at the base of machine.

Reconnect
the lid switch harness then push the retaining clips back down into position
to secure the cabinet to the rear of the machine. Reinstall and secure
the console to complete the repair.

Kenmore / Whirlpool top load, direct drive washers use a "Motor Coupler" between the motor and transmission. It's used as a fail safe device and consists of three parts. Two of the parts are the same, plastic units with three prongs that fit on one of the motor output shafts and the other on the transmission input shaft. Between them is a rubber piece with six holes. The power from the motor is transmitted through the rubber piece to the transmission.

The other shaft on the motor directly drives the pump.

If the motor coupler is broken, or worn, the motor may not be able to send full power to the transmission for agitating or spinning and may produce a whining noise.

See the following for how to remove the cabinet, pump, motor and motor mounting plate to inspect and replace the motor coupler.

Could be a restriction in the drain line. You would be surprised at what can get into the drain lines.

With the machine empty, tilt it back enough so that you can get access to the bottom. Brace the machine so it won't fall. If there is a bottom soft panel please remove it. The water pump is located on the bottom of the motor. (It will be either white or grey.) Remove the hoses from the pump. (You are going to get a little wet.) check to see if there is any restrictions in the hoses. (I do this by blowing through them but you may want to do this in another way.) To check the pump, follow the motor toward the transmission. There is a coupler that connects the motor to the transmission. Turn this coupler by hand a listen to the pump. If there is any objects in the pump then replace the pump.

Also, while your under the machine it would be a good idea to check the motor coupler. Move it back and forth and check for any play in the coupler. If there is too much play then the coupler needs replaced. (A coupler that it severely worn can cause the same problem and still let the machine work.